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Some Korovkin type approximation applications of power series methods

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Abstract

Korovkin type approximation via summability methods is one of the recent interests of the mathematical analysis. In this paper, we prove some Korovkin type approximation theorems in \(L_{q}[a,b]\), the space of all measurable real valued qth power Lebesgue integrable functions defined on [a, b] for \(q\ge 1\), and C[a, b], the space of all continuous real valued functions defined on [a, b], via statistical convergence with respect to power series (summability) methods, integral summability methods and \(\mu \)-statistical convergence of the power series transforms of positive linear operators. We also show with examples that the results obtained in the present paper are stronger than some existing approximation theorems in the literature.

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Acknowledgements

The research of Havva Uluçay has been supported by Turkish Scientific and Technological Research Council (TÜBİTAK) Programme 2211.

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Authors and Affiliations

  1. Department of Mathematics, Faculty of Science and Letters, Istanbul Technical University, 34469, Istanbul, Sariyer, Turkey

    Havva Uluçay

  2. Department of Mathematics, Faculty of Science, Ankara University, 06100, Ankara, Beşevler, Turkey

    Mehmet Ünver

  3. Department of Mathematics, Faculty of Science, Selçuk University, 42003, Konya, Selcuklu, Turkey

    Dilek Söylemez

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  1. Havva Uluçay
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  2. Mehmet Ünver
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Correspondence to Mehmet Ünver.

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Uluçay, H., Ünver, M. & Söylemez, D. Some Korovkin type approximation applications of power series methods. Rev. Real Acad. Cienc. Exactas Fis. Nat. Ser. A-Mat. 117, 24 (2023). https://doi.org/10.1007/s13398-022-01360-z

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